Exact Membership Functions for the Fuzzy Weighted Average

P.M. van den Broek, J.A.R. Noppen

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    2 Citations (Scopus)
    21 Downloads (Pure)

    Abstract

    The problem of computing the fuzzy weighted average, where both attributes and weights are fuzzy numbers, is well studied in the literature. Generally, the approach is to apply Zadeh’s extension principle to compute α-cuts of the fuzzy weighted average from the α-cuts of the attributes and weights for fixed values of α∈[0..1]; this means that all values of the membership functions of the fuzzy weighted average are computed separately. In this paper, we generalise this approach in such a way that α is considered to be a parameter; this enables us to compute exact analytical membership functions for the fuzzy weighted average in case the attributes and weights are triangular or trapeizoidal fuzzy numbers. To illustrate the power of our algorithms, they are applied to the examples from the literature, providing exact membership functions in each case.
    Original languageUndefined
    Title of host publicationComputational Intelligence
    Place of PublicationBerlin / Heidelberg
    PublisherSpringer
    Pages85-99
    Number of pages15
    ISBN (Print)978-3-642-20206-3
    DOIs
    Publication statusPublished - 2011

    Publication series

    NameStudies in Computational Intelligence
    PublisherSpringer
    Number343
    Volume343
    ISSN (Print)1860-949X
    ISSN (Electronic)1860-9503

    Keywords

    • METIS-278714
    • IR-77052
    • EWI-20154
    • Fuzzy weighted average
    • membership functions

    Cite this

    van den Broek, P. M., & Noppen, J. A. R. (2011). Exact Membership Functions for the Fuzzy Weighted Average. In Computational Intelligence (pp. 85-99). (Studies in Computational Intelligence; Vol. 343, No. 343). Berlin / Heidelberg: Springer. https://doi.org/10.1007/978-3-642-20206-3_6